貨運百科

標題:

因式分解(8) 送20分

發問:

1. (x-y)^2-(x-z)^2 2. (a+b+c)^2-d^2 3. (3x+2)^2-(2x+1)^2 4. 9y^2-(2x-y)^2 5. (x-3y)^2-(y-x)^2 6. (3x-y)^2-(5x-3y)^2 7. 25x^2-(x+2y+4z)^2 8. 4x^2+4x+1 9. x^2+2x+1-y^2 10. a^2-2ab+b^2-9x^2 11. x^2-a^2-2ab-b^2

最佳解答:

1(x-y)2 -(x-z)2 =[(x-y)-(x-z)][(x-y)+(x-z)] =(z-y)(x-y-z) 2. (a+b+c)2 -d2 =[(a+b+c)-d][(a+b+c)+d] =(a+b+c-d)(a+b+c+d) 3. (3x+2)2 -(2x+1)2 =[(3x+2)-(2x+1)][(3x+2)+(2x+1)] =(x+1)(5x+3) 4. 9y2 -(2x-y)2 =(3y)2 -(2x-y)2 =[(3y)+(2x-y)][(3y)-(2x-y)] 5. (x-3y)2 -(y-x)2 =[(x-3y)+(y-x)][ (x-3y)-(y-x)] =(-2y)(2x-4y) =-4y(x-2y) 6. (3x-y)2 -(5x-3y)2 =[(3x-y)-(5x-3y)][(3x-y)+(5x-3y)] =(-2x+2y)(8x-4y) =-8(x-y)(2x-y) 7. 25x2 -(x+2y+4z)2 = (5x)2 -(x+2y+4z)2 =[(5x)-(x+2y+4z)][ (5x)+(x+2y+4z)] =(4x-2y-4z)(6x+2y+4z) =4(2x-y-2z)(3x+y+2z) 8. 4x2 +4x+1 =(2x)2 +4x+1 =(2x+1)2 9. x2 +2x+1-y2 =(x+1)^2-y2 =[(x+1)-y][ (x+1)+y] =(x-y+1)(x+y+1) 10. a2 -2ab+b2 -9x2 =(a-b)2 -(3x)2 =[(a-b)-(3x)][(a-b)+(3x)] =(a-b-3x)(a-b+3x) 11. x2 -a2 -2ab-b2 =x2 -( a2 +2ab+b2 ) = x2 -(a+b)2 =[ x-(a+b)][x+(a+b)] =(x-a-b)(x+a+b)

其他解答:

4. 9y2 -(2x-y)2 =(3y)2 -(2x-y)2 =[(3y)+(2x-y)][(3y)-(2x-y)] =[2y+2x][4y-2x] =4(y+x)(2y-x)

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